The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
08 Mar 1998-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 454, Iss: 1971, pp 903-995
TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...
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TL;DR: The current state-of-the-art in structured light profilometry systems is described, as well as the main advancements in hardware technology and coding strategy that have led to their successful development.
286 citations
Cites methods from "The empirical mode decomposition an..."
...Finally, empirical mode 227 decomposition (EMD) [48,49] or principle component analysis (PCA) [50] techniques were 228 introduced in FTP to extract the fundamental frequency band and to remove the non-linear 229 carrier frequency caused by divergent illumination without the need for capturing multiple fringe 230 patterns....
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TL;DR: A new model which is fully specified for automated seizure onset detection and seizure onset prediction based on electroencephalography (EEG) measurements is proposed which could outperform the state-of-the art models.
286 citations
TL;DR: Experimental results show that the proposed transfer learning approach for fault diagnosis with neural networks can improve the classification accuracy and reduce the training time comparing with the conventional neural network method when there are only a small amount of target data.
Abstract: Traditional machine learning algorithms have made great achievements in data-driven fault diagnosis. However, they assume that all the data must be in the same working condition and have the same distribution and feature space. They are not applicable for real-world working conditions, which often change with time, so the data are hard to obtain. In order to utilize data in different working conditions to improve the performance, this paper presents a transfer learning approach for fault diagnosis with neural networks. First, it learns characteristics from massive source data and adjusts the parameters of neural networks accordingly. Second, the structure of neural networks alters for the change of data distribution. In the same time, some parameters are transferred from source task to target task. Finally, the new model is trained by a small amount of target data in another working condition. The Case Western Reserve University bearing data set is used to validate the performance of the proposed transfer learning approach. Experimental results show that the proposed transfer learning approach can improve the classification accuracy and reduce the training time comparing with the conventional neural network method when there are only a small amount of target data.
286 citations
Cites methods from "The empirical mode decomposition an..."
...Lei et al. [28] proposed a mechanical fault diagnosis model based on WPD and EMD....
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...Wavelet Package Decomposition (WPD) [26] and Empirical Mode Decomposition (EMD) [27] are commonly used methods for signal preprocessing and feature extraction....
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TL;DR: In this paper, the authors show that global mean sea level (GMSL) has been rising at a faster rate during the satellite altimetry period (1993-2014) than previous decades, and is expected to accelerate further over the coming century.
Abstract: Global mean sea level (GMSL) has been rising at a faster rate during the satellite altimetry period (1993–2014) than previous decades, and is expected to accelerate further over the coming century. However, the accelerations observed over century and longer periods have not been clearly detected in altimeter data spanning the past two decades. Here we show that the rise, from the sum of all observed contributions to GMSL, increases from 2.2 ± 0.3 mm yr−1 in 1993 to 3.3 ± 0.3 mm yr−1 in 2014. This is in approximate agreement with observed increase in GMSL rise, 2.4 ± 0.2 mm yr−1 (1993) to 2.9 ± 0.3 mm yr−1 (2014), from satellite observations that have been adjusted for small systematic drift, particularly affecting the first decade of satellite observations. The mass contributions to GMSL increase from about 50% in 1993 to 70% in 2014 with the largest, and statistically significant, increase coming from the contribution from the Greenland ice sheet, which is less than 5% of the GMSL rate during 1993 but more than 25% during 2014. The suggested acceleration and improved closure of the sea-level budget highlights the importance and urgency of mitigating climate change and formulating coastal adaption plans to mitigate the impacts of ongoing sea-level rise.
284 citations
TL;DR: In this paper, a combined model combining complete ensemble empirical mode decomposition adaptive noise (CEEMDAN), flower pollination algorithm with chaotic local search (CLSFPA), five neural networks and no negative constraint theory (NNCT) is proposed for short-term wind speed forecasting.
282 citations
References
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TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
16,554 citations
"The empirical mode decomposition an..." refers background in this paper
...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
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Book•
01 Jan 1974
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.
8,808 citations
Book•
01 Jan 1971
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Abstract: From the Publisher:
A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems. With more than 100,000 copies in print and six foreign translations, the first edition standardized the methodology in this field. This new edition covers all new procedures developed since 1971 and extends the application of random data analysis to aerospace and automotive research; digital data analysis; dynamic test programs; fluid turbulence analysis; industrial noise control; oceanographic data analysis; system identification problems; and many other fields. Includes new formulas for statistical error analysis of desired estimates, new examples and problem sets.
6,693 citations
"The empirical mode decomposition an..." refers background in this paper
...A brief tutorial on the Hilbert transform with the emphasis on its physical interpretation can be found in Bendat & Piersol (1986)....
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01 Jan 1946
5,910 citations
"The empirical mode decomposition an..." refers methods in this paper
...In order to obtain meaningful instantaneous frequency, restrictive conditions have to be imposed on the data as discussed by Gabor (1946), Bedrosian (1963) and, more recently, Boashash (1992): for any function to have a meaningful instantaneous frequency, the real part of its Fourier transform has…...
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TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Abstract: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22
5,806 citations
"The empirical mode decomposition an..." refers background in this paper
...In general, if more quantitative results are desired, the original skeleton presentation is better; if more qualitative results are desired, the smoothed presentation is better....
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...Therefore, the parameter, ν, defined as N21 −N20 = 1 π2 m4m0 −m22 m2m0 = 1 π2 ν2, (3.7) offers a standard bandwidth measure (see, for example, Rice 1944a, b, 1945a, b; Longuet-Higgins 1957)....
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